Home
Class 12
MATHS
Prove that the curves x = y^(2) and xy =...

Prove that the curves `x = y^(2)` and xy = k cut at right angles* if `8k^(2) = 1`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT BANGLISH|Exercise EXERCISE 6.4|23 Videos

  • APPLICATION OF DERIVATIVES

    NCERT BANGLISH|Exercise EXERCISE 6.5|48 Videos

  • APPLICATION OF DERIVATIVES

    NCERT BANGLISH|Exercise EXERCISE 6.2|23 Videos

  • APPLICATION OF INTEGRALS

    NCERT BANGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Show that the curves x=y^(2) and xy=k cut at right angles, if 8k^(2)=1

Show that x=y^2 and xy = k cut orthogonally if 8k^2=1

If the curves y^(2)= 4x and xy = k cut orthogonally, then the value of k^(2) will be-

Show that curves x^(3)-3xy^(2)+2=0 and y^(3)-3x^(2)y+2=0 intersect at right angles.

Prove that the straight lines joining the origin to the points of intersection of the straight line hx+ky=2hk and the curve (x-k)^(2)+(y-h)^(2)=c^(2) are at right angle if h^(2)+k^(2)=c^(2) .

The area of the region bounded by the curves y=x^(2),y=|2-x^(2)| and y=2 which lies to the right of the line x=1, is

The curves x^2/a+y^2/b=1 and x^2/a_1+y^2/b_1=1 will cut orthogonally if (a-b) =

Find the condition for the line y= mx to cut at right angles the conic ax^(2)+2hxy+by^(2)=1.

Which one of the following curves cut the parabola y^2 =4ax at right angles? x^2+y^2=a^2 (b) y=e^(-x//2a) y=a x (d) x^2=4a y

Show that the tangents to the curve y=x^2-5x+6 at the point (2,0) and (3,0) are at right angle.

NCERT BANGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.3
  1. Find the equations of all lines having slope 0 which are tangent to th...

    Text Solution

    |

  2. Find points on the curve (x^(2))/(9) +(y^(2))/(16) =1 at which the tan...

    Text Solution

    |

  3. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  4. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  5. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  6. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  7. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  8. Find the equation of the tangent line to the curve y = x^(2) – 2x +7 w...

    Text Solution

    |

  9. Show that the tangents to the curve y = 7x^(3) + 11 at the points wher...

    Text Solution

    |

  10. Find the points on the curve y = x^(3) at which the slope of the tange...

    Text Solution

    |

  11. For the curve y = 4x^(3) – 2x^(5) , find all the points at which the t...

    Text Solution

    |

  12. Find the points on the curve x^(2) + y^(2) – 2x – 3 = 0 at which the t...

    Text Solution

    |

  13. Find the equation of the normal at the point (am^(2) ,am^(3) ) for the...

    Text Solution

    |

  14. Find the equation of the normals to the curve y = x^(3) + 2x + 6 which...

    Text Solution

    |

  15. Find the equations of the tangent and normal to the parabola y^(2) = 4...

    Text Solution

    |

  16. Prove that the curves x = y^(2) and xy = k cut at right angles* if 8k^...

    Text Solution

    |

  17. Find the equations of the tangent and normal to the hyperbola (x^(2))/...

    Text Solution

    |

  18. Find the equation of the tangent to the curve y= sqrt(3x-2) which is p...

    Text Solution

    |

  19. The slope of the normal to the curve y = 2x^(2) + 3 sin x at x = 0 is

    Text Solution

    |

  20. The line y = x + 1 is a tangent to the curve y^(2) = 4x at the point

    Text Solution

    |